The “Aristotelian pQ-lattices” are the combinatorial outcomes of Moretti’s “Aristotelian pQ-semantics”. As such they display order-theoretically the possible “opposition qualities” (a generalisation of the classical notions of “contradiction”, “contrariety”, “subcontrariety” and “subalternation”, reconduced by Moretti to the notions of “Aristotelian (2 power 2)-semantics” and “Aristotelian (2 power 2)-lattice”).